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Math Coach Amy
Amy Ferguson Moncure

7th Grade Math · Unit 6

Angles in
Similar Figures

Triangle angles sum to 180°. Quadrilateral angles sum to 360°. Similar figures copy those angle measures.

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Key Ideas Easy Medium Hard
What to Remember

Triangle sum

The angles of a triangle sum to 180°.

Subtract the two given angles from 180° to get the third angle.

Quadrilateral sum

The angles of a quadrilateral sum to 360°.

Subtract the three given angles from 360° to get the fourth angle.

Similar copies

Matching angles of similar figures are equal.

A similar triangle has the same three angles. A similar quadrilateral has the same four angles.

Name the match

Use ∠ when you name an angle.

The third angle of the first triangle is the same measure as the matching angle of the similar triangle.

Level 1

Easy

Find the third angle of a triangle.

Example
One triangle has angles 40° and 60°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?

Angles of a triangle sum to 180°.

40° + 60° + unknown = 180°

unknown = 180° − 100°

unknown = 80°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 80°

1
One triangle has angles 50° and 60°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

50° + 60° + unknown = 180°

unknown = 180° − 110°

unknown = 70°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 70°

2
One triangle has angles 30° and 40°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

30° + 40° + unknown = 180°

unknown = 180° − 70°

unknown = 110°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 110°

3
One triangle has angles 45° and 45°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

45° + 45° + unknown = 180°

unknown = 180° − 90°

unknown = 90°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 90°

4
One triangle has angles 35° and 55°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

35° + 55° + unknown = 180°

unknown = 180° − 90°

unknown = 90°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 90°

5
One triangle has angles 20° and 30°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

20° + 30° + unknown = 180°

unknown = 180° − 50°

unknown = 130°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 130°

6
One triangle has angles 70° and 50°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

70° + 50° + unknown = 180°

unknown = 180° − 120°

unknown = 60°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 60°

7
One triangle has angles 25° and 65°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

25° + 65° + unknown = 180°

unknown = 180° − 90°

unknown = 90°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 90°

8
One triangle has angles 80° and 40°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

80° + 40° + unknown = 180°

unknown = 180° − 120°

unknown = 60°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 60°

9
One triangle has angles 15° and 75°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

15° + 75° + unknown = 180°

unknown = 180° − 90°

unknown = 90°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 90°

10
One triangle has angles 55° and 65°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

55° + 65° + unknown = 180°

unknown = 180° − 120°

unknown = 60°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 60°

Level 2

Medium

The similar triangle has the same angles.

Example
One triangle has angles 48° and 72°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?

Angles of a triangle sum to 180°.

48° + 72° + unknown = 180°

unknown = 180° − 120°

unknown = 60°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 60°

1
One triangle has angles 36° and 72°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

36° + 72° + unknown = 180°

unknown = 180° − 108°

unknown = 72°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 72°

2
One triangle has angles 28° and 62°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

28° + 62° + unknown = 180°

unknown = 180° − 90°

unknown = 90°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 90°

3
One triangle has angles 33° and 57°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

33° + 57° + unknown = 180°

unknown = 180° − 90°

unknown = 90°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 90°

4
One triangle has angles 42° and 68°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

42° + 68° + unknown = 180°

unknown = 180° − 110°

unknown = 70°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 70°

5
One triangle has angles 24° and 96°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

24° + 96° + unknown = 180°

unknown = 180° − 120°

unknown = 60°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 60°

6
One triangle has angles 18° and 72°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

18° + 72° + unknown = 180°

unknown = 180° − 90°

unknown = 90°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 90°

7
One triangle has angles 51° and 39°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

51° + 39° + unknown = 180°

unknown = 180° − 90°

unknown = 90°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 90°

8
One triangle has angles 64° and 58°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

64° + 58° + unknown = 180°

unknown = 180° − 122°

unknown = 58°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 58°

9
One triangle has angles 27° and 63°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

27° + 63° + unknown = 180°

unknown = 180° − 90°

unknown = 90°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 90°

10
One triangle has angles 44° and 46°. Find the third angle. A similar triangle matches this one. What is the angle that matches the third angle?
Show Answer

Angles of a triangle sum to 180°.

44° + 46° + unknown = 180°

unknown = 180° − 90°

unknown = 90°

Similar triangles have matching angles equal, so the similar triangle uses these same measures.

Answer: 90°

Level 3

Hard

Find the fourth angle. A similar quadrilateral has the same angles.

Example
The quadrilaterals are similar. Three angles of a quadrilateral measure 80°, 90°, and 100°. Find the fourth angle.

The interior angles of a quadrilateral sum to 360°.

80° + 90° + 100° + unknown = 360°

unknown = 360° − 270°

unknown = 90°

A similar quadrilateral has these same four angles.

Answer: 90°

1
The quadrilaterals are similar. Three angles of a quadrilateral measure 70°, 80°, and 90°. Find the fourth angle.
Show Answer

The interior angles of a quadrilateral sum to 360°.

70° + 80° + 90° + unknown = 360°

unknown = 360° − 240°

unknown = 120°

A similar quadrilateral has these same four angles.

Answer: 120°

2
The quadrilaterals are similar. Three angles of a quadrilateral measure 60°, 70°, and 80°. Find the fourth angle.
Show Answer

The interior angles of a quadrilateral sum to 360°.

60° + 70° + 80° + unknown = 360°

unknown = 360° − 210°

unknown = 150°

A similar quadrilateral has these same four angles.

Answer: 150°

3
The quadrilaterals are similar. Three angles of a quadrilateral measure 100°, 80°, and 70°. Find the fourth angle.
Show Answer

The interior angles of a quadrilateral sum to 360°.

100° + 80° + 70° + unknown = 360°

unknown = 360° − 250°

unknown = 110°

A similar quadrilateral has these same four angles.

Answer: 110°

4
The quadrilaterals are similar. Three angles of a quadrilateral measure 50°, 60°, and 70°. Find the fourth angle.
Show Answer

The interior angles of a quadrilateral sum to 360°.

50° + 60° + 70° + unknown = 360°

unknown = 360° − 180°

unknown = 180°

A similar quadrilateral has these same four angles.

Answer: 180°

5
The quadrilaterals are similar. Three angles of a quadrilateral measure 90°, 90°, and 80°. Find the fourth angle.
Show Answer

The interior angles of a quadrilateral sum to 360°.

90° + 90° + 80° + unknown = 360°

unknown = 360° − 260°

unknown = 100°

A similar quadrilateral has these same four angles.

Answer: 100°

6
The quadrilaterals are similar. Three angles of a quadrilateral measure 110°, 70°, and 60°. Find the fourth angle.
Show Answer

The interior angles of a quadrilateral sum to 360°.

110° + 70° + 60° + unknown = 360°

unknown = 360° − 240°

unknown = 120°

A similar quadrilateral has these same four angles.

Answer: 120°

7
The quadrilaterals are similar. Three angles of a quadrilateral measure 95°, 85°, and 75°. Find the fourth angle.
Show Answer

The interior angles of a quadrilateral sum to 360°.

95° + 85° + 75° + unknown = 360°

unknown = 360° − 255°

unknown = 105°

A similar quadrilateral has these same four angles.

Answer: 105°

8
The quadrilaterals are similar. Three angles of a quadrilateral measure 40°, 50°, and 60°. Find the fourth angle.
Show Answer

The interior angles of a quadrilateral sum to 360°.

40° + 50° + 60° + unknown = 360°

unknown = 360° − 150°

unknown = 210°

A similar quadrilateral has these same four angles.

Answer: 210°

9
The quadrilaterals are similar. Three angles of a quadrilateral measure 120°, 80°, and 50°. Find the fourth angle.
Show Answer

The interior angles of a quadrilateral sum to 360°.

120° + 80° + 50° + unknown = 360°

unknown = 360° − 250°

unknown = 110°

A similar quadrilateral has these same four angles.

Answer: 110°

10
The quadrilaterals are similar. Three angles of a quadrilateral measure 65°, 75°, and 85°. Find the fourth angle.
Show Answer

The interior angles of a quadrilateral sum to 360°.

65° + 75° + 85° + unknown = 360°

unknown = 360° − 225°

unknown = 135°

A similar quadrilateral has these same four angles.

Answer: 135°

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